The CIRP survey includes questions about students’ backgrounds, activities, and attitudes. In one question, students were asked their “current religious preference” and given a choice of seventeen common religions and Christian denominations, “Other Christian,” “Other religion,” or “None.” Another question asked students how often they “attended a religious service” in the last year. The choices were “Frequently,” “Occasionally,” and “Not at all.” The instructions directed students to select “Occasionally” if they attended one or more times, so a nonobservant student who attended a wedding and a funeral (and follows instructions) would not be counted among the apostates.

The following figure shows students' responses over the history of the survey (updated with the most recent data):

Here's what I said about this figure 4 years ago:

The number of students with no religious preference has been increasing steadily since the low point ... in 1978. ... The rate of growth from 1980 to the present has been between 0.25 and 0.35 percentage points per year... Since 1997, the rate may have increased to 0.6 or 0.7 percentage points per year. At that rate, the class of 2056 will have an atheist majority.

A linear extrapolation from data like this is mostly ridiculous, but as it turns out the next four points are pretty much in line. And finally, I claimed:

Both curves show a possible acceleration between 2005 and 2006. This jump may be due to increased visibility of atheism following the publication of books by Sam Harris, Daniel C. Dennett, and Richard Dawkins.

That last point is pure speculation on my part, but it is also what you might call a testable hypothesis. Which gives me an excuse to talk about another article of mine, "A novel changepoint detection algorithm," which you can download from arXiv. Here's the abstract:

We [my imaginary co-author and I] propose an algorithm for simultaneously detecting and locating changepoints in a time series, .... The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i.

In a time series, a changepoint is a time where the behavior of the system changes abruptly. By applying my algorithm to the CIRP data, we can test whether there are changepoints and when they are likely to have occurred.

My conjecture is that the rate of increase changed in 1997 and maybe again in 2006. Since this is a hypothesis about rates, I'll start by computing differences between successive elements as an estimate of the first derivative. Where there is missing data, I use the average yearly change. This figure shows the result:

As usual, taking differences amplifies noise and makes it harder to see patterns. But that's exactly what my algorithm (which is mine) is good for. Here are the results:

The y-axis is the probability that the last (most recent) change point occurred during a given year, accumulated from right to left. The gray lines indicate years with a relatively high probability of being the last changepoint. So, reading from right to left, there is a 5% chance of a changepoint in 2006 and a 5% chance for 1998. The most likely location of the last changepoint is 1984 (about 20%) or 1975 (25%). So that provides little if any evidence for my conjecture, which is pretty much what I deserve.

A simpler, and more likely, hypothesis is that the trend is accelerating; that is, the slope is changing continuously, not abruptly. And that's easy to test by fitting a line to the yearly changes.

The red line shows the linear least squares fit, with slope 0.033; the p-value (chance of seeing an absolute slope as big as that) is 0.006, so you can either reject the null hypothesis or update your subjective degree of belief accordingly.

The fitted value for the current rate of growth is 0.9 percentage points per year, accelerating at 0.033 percentage points per year^2. So here's my prediction: in 2011 the percentage of freshman who report no religious affiliation will be 23.0 + 0.9 + 0.03 = 23.9%.

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If you find this sort of thing interesting, you might like my free statistics textbook, Think Stats. You can download it or read it at thinkstats.com.